Carp can handle whatever high temps you throw at them, the only result being the sluggishness that you observed. If I remember correctly, the high range before they begin to taper off in their activities is somewhere in the mid 80s (surface).

I'm glad that the nymph is working so well for you. Being a beadhead, are you letting it sink to the bottom ahead of a feeding fish and then twitching it? I'm curious because the most interest that the carp I've seen take in a nymph was towards an unweighted fly. It was cast ahead of the fish and given ample time to get to the bottom, and when the fish approached a few gentle strips moved the fly along. It stayed barely above bottom, but not bottom.

I'm just curious. By the way, the unweighted nymph hasn't taken a carp yet, so maybe the beadhead is the key.